Error analysis and numerical solution of generalized Benjamin–Bona–Mahony–Burgers equation using 3-scale Haar wavelets

Abstract

In this paper, we propose an extended numerical algorithm for the numerical solution of the Benjamin–Bona–Mahony–Burgers equation. This algorithm involves the application of wavelet theory. First, we use the Quasilinearization technique of linearization and apply the 3-scale Haar wavelet approach for truncation error. This algorithm is constructed from two wavelet functions that make it robust and highly accurate. A multi-resolution is used to generate the Haar basis function. We consider three cases of a mathematical problem for the accuracy of the presented algorithm. The obtained results show good agreement with analytical solutions and have better accuracy.

Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation

“…Lately, the B-spline collocation method with quadratic B-spline [4], cubic B-spline (CB) [6][7][8], cubic trigonometric B-spline (CTB) [9][10][11], and extended cubic B-spline (ECB) [12][13][14][15][16] have been formulated successfully on some differential equations with accurate results and high efficiency. There are several techniques used to handle the nonlinear term in the BBME namely Taylor series expansion [17], quasilinearization [18] and Adomian polynomials [19]. This article aims to solve the BBME using the Besse ECB collocation method without linearizing the algebraic system.…”